[permalink] [id link]

Every complemented distributive lattice has a unique orthocomplementation and is in fact a Boolean algebra.

from
Wikipedia

## Some Related Sentences

Every and complemented

__Every__Saturday,

**a**wide variety of producers from around the country take part

**in**the very popular market selling quality produce including

**a**huge array of hot foods,

__complemented__by many others selling hand-made jewellery, gifts, childrenswear

**and**vintage clothing

**.**

Every and distributive

__Every__

**Boolean**

**algebra**

**is**

**a**Heyting

**algebra**when

**a**→ b

**is**defined as usual as ¬

**a**∨ b, as

**is**every complete

__distributive__

**lattice**when

**a**→ b

**is**taken to be the supremum of the set of all c for which

**a**∧ c ≤ b

**.**The open sets of

**a**topological space form

**a**complete

__distributive__

**lattice**

**and**hence

**a**Heyting

**algebra**

**.**

Every and lattice

__Every__

__lattice__element of the structure

**is**

**in**its proper place, whether it

**is**

**a**single atom or

**a**molecular grouping

**.**

*

__Every__totally ordered set that**is****a**bounded__lattice__**is**also**a**Heyting**algebra**, where**is**equal to when,**and**1 otherwise**.**__Every__complete

__lattice__

**is**also

**a**bounded

__lattice__, which

**is**to say that it

**has**

**a**greatest

**and**least element

**.**

__Every__

__lattice__

**in**can be generated from

**a**basis for the vector space by forming all linear combinations with integer coefficients

**.**

*

__Every__substructure**is**the union of its finitely generated substructures ; hence Sub ( A )**is**an algebraic__lattice__**.**
Also,

**a**kind of converse holds:__Every__algebraic__lattice__**is**isomorphic to Sub ( A ) for some**algebra**A**.**__Every__quasinormal subgroup

**is**

**a**modular subgroup, that

**is**,

**a**modular element

**in**the

__lattice__of subgroups

**.**

Every and has

__Every__woman

__has__had the experience of saying no when she meant yes,

**and**saying yes when she meant no

**.**

__Every__detail

**in**his interpretation

__has__been beautifully thought out,

**and**of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he

**is**playing with Viennese musicians ),

**and**the gossamer shading throughout

**.**

__Every__family of Riviera Presbyterian Church

__has__been asked to read the Bible

**and**pray together daily during National Christian Family Week

**and**to undertake one project

**in**which all members of the family participate

**.**

__Every__community, if it

**is**alive

__has__

**a**spirit,

**and**that spirit

**is**the center of its unity

**and**identity

**.**

__Every__such subset

__has__

**a**smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set

**.**

** Zorn's lemma:

__Every__non-empty partially ordered set**in**which every chain ( i**.**e**.**totally ordered subset )__has__an upper bound contains at least one maximal element**.**
The restricted principle "

__Every__partially ordered set__has__**a**maximal totally ordered subset "**is**also equivalent to AC over ZF**.**
** Tukey's lemma:

__Every__non-empty collection of finite character__has__**a**maximal element with respect to inclusion**.**
*

__Every__continuous functor on**a**small-complete category which satisfies the appropriate solution set condition__has__**a**left-adjoint ( the Freyd adjoint functor theorem ).__Every__unit of length

__has__

**a**corresponding unit of area, namely the area of

**a**square with the given side length

**.**

__Every__field

__has__an algebraic extension which

**is**algebraically closed ( called its algebraic closure ), but proving this

**in**general requires some form of the axiom of choice

**.**

__Every__ATM cell

__has__an 8-or 12-bit Virtual Path Identifier ( VPI )

**and**16-bit Virtual Channel Identifier ( VCI ) pair defined

**in**its header

**.**

Every and unique

__Every__other aspect of film making originated

**in**

**a**different medium than film ( photography, art direction, writing, sound recording ), but editing

**is**the one process that

**is**

__unique__to film

**.**

__Every__species can be given

**a**

__unique__(

**and**, one hopes, stable ) name, as compared with common names that are often neither

__unique__nor consistent from place to place

**and**language to language

**.**

__Every__LORAN chain

**in**the world uses

**a**

__unique__Group Repetition Interval, the number of which, when multiplied by ten, gives how many microseconds pass between pulses from

**a**given station

**in**the chain

**.**

__Every__non-negative real number

**a**

**has**

**a**

__unique__non-negative square root, called the principal square root, which

**is**denoted by, where √

**is**called the radical sign or radix

**.**

__Every__element s, except

**a**possible greatest element,

**has**

**a**

__unique__successor ( next element ), namely the least element of the subset of all elements greater than s

**.**

__Every__subset which

**has**an upper bound

**has**

**a**least upper bound

**.**

__Every__well-ordered set

**is**uniquely order isomorphic to

**a**

__unique__ordinal number, called the order type of the well-ordered set

**.**

__Every__system

**is**

__unique__to the business drivers it supports, therefore the quality attributes of each system such as fault-tolerance, backward compatibility, extensibility, reliability, maintainability, availability, security, usability,

**and**such other – ilities will vary with each implementation

**.**

__Every__Gundam

**has**

**a**

__unique__name that befits the nature of the suit

**and**/ or its origins, such as the XXXG-01W Wing Gundam, XXXG-01D Gundam Deathscythe

**and**the XXXG-01S Shenlong Gundam

**.**

* PASSIA Diaries

**and**Annual Reports:__Every__year since 1988, PASSIA publishes its “ Diary ”,**a**__unique__annual resource book combining**a**comprehensive directory of contact information for Palestinian**and**interna tional institu tions operating**in**Palestine,**a**day-to-day calendar,**and**an agenda containing facts**and**figures, graphs, statistics, chronologies**and**maps related to Palestine**and**the Palestinians**.**__Every__composite number can be written as the product of two or more ( not necessarily distinct ) primes ; furthermore, this representation

**is**

__unique__up to the order of the factors

**.**

__Every__crystalline solid will have

**a**

__unique__pattern of d-spacings ( known as the powder pattern ), which

**is**

**a**“ finger print ” for that solid

**.**

One

__unique__challenge that the team encountered early on was related to deph perception, the team remedied through the use of shadows:__Every__object**in**the game**has****a**shadow directly below it regardless of the area's lighting**.**__Every__June this area

**is**inundated with the Ronceverte River Festival, where

**a**

__unique__raffle

**is**held by floating hundreds of small, numbered yellow ducks into the river

**.**

__Every__device on the bus

**has**

**a**

__unique__5-bit primary address,

**in**the range from 0 to 30 ( 31 total possible addresses ).

__Every__

__unique__cultivar

**has**

**a**

__unique__name within its denomination class ( which

**is**almost always the genus ).

0.268 seconds.